I am taking an online course where vectors are typically written out as column vectors. It seems like the only row vectors we have seen are the transposes of column vectors and labeled as such.

So I'm wondering if mathematicians (at least those in linear algebra) tend to favor column vectors. This is essentially a question about convention, i.e. is it such a strong convention that if you told a mathematician about a vector without specifying its alignment, would they assume it is a column vector?

Come to think of it I guess that might make sense since it is the first dimension.